CN111200383B - Method for high-precision online observation of resistance and flux linkage of induction motor rotor - Google Patents
Method for high-precision online observation of resistance and flux linkage of induction motor rotor Download PDFInfo
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- CN111200383B CN111200383B CN202010037397.7A CN202010037397A CN111200383B CN 111200383 B CN111200383 B CN 111200383B CN 202010037397 A CN202010037397 A CN 202010037397A CN 111200383 B CN111200383 B CN 111200383B
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/13—Observer control, e.g. using Luenberger observers or Kalman filters
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P21/00—Arrangements or methods for the control of electric machines by vector control, e.g. by control of field orientation
- H02P21/14—Estimation or adaptation of machine parameters, e.g. flux, current or voltage
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- H—ELECTRICITY
- H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
- H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
- H02P2207/00—Indexing scheme relating to controlling arrangements characterised by the type of motor
- H02P2207/01—Asynchronous machines
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Abstract
The invention provides a method for high-precision online observation of rotor resistance and flux linkage of an induction motor, relates to the field of induction motor parameter identification, and aims to improve the observation precision of induction motor parameters and the robustness of a system. The inductance of the induction motor is affected by saturation, and the value of the inductance changes along with the working condition change of the motor; the resistance is affected by temperature, skin effect and proximity effect, and the value change is more complicated. In the prior art, only the influence of the resistance on the temperature is considered mostly, the saturation of the used induction motor model is not considered, and the observation precision of the rotor flux linkage of the induction motor is influenced by the inconsistency of the model and an actual controlled object. The method provided by the patent combines the system state observer and the PI controller, is completely based on the saturated model of the induction motor, can accurately observe the rotor resistance under the influence of various factors in real time, and improves the observation precision of the rotor resistance and flux linkage of the induction motor and the robustness of the system.
Description
Technical Field
The invention relates to the technical field of induction motor parameter identification, in particular to a method for high-precision online observation of resistance and flux linkage of an induction motor rotor.
Background
In industrial applications, vector control is widely used for induction motors. In order to obtain a high performance vector control effect of the induction motor, the d-axis of the dq-axis in the vector control needs to be accurately aligned with the induction motor flux linkage. The flux linkage of an induction motor is not directly measurable by a sensor, and therefore, needs to be estimated with high precision. Induction motors, when fitted with a rotational speed sensor, typically orient the d-axis of the dq-axis to the rotor flux linkage.
The estimation accuracy of the rotor flux linkage is affected by the accuracy of the rotor resistance value and the rotor inductance value. If the rotor resistance value, or the rotor inductance value, deviates from the actual value, the calculated rotor flux linkage has an error from the actual value, which degrades the performance of the vector control.
The inductor is influenced by the saturation degree of the motor, and the resistor part is influenced by the temperature, and the resistor part are changed at any time when the motor runs. This therefore increases the difficulty of estimating the rotor flux linkage. The inductance value affected by saturation can be found from the magnetization curve of the induction machine. By installing a heat sensor on the rotor and correcting the resistance value of the rotor by temperature, the observation accuracy of the rotor flux linkage can be improved to a certain extent. However, this not only increases the cost, but also reduces the reliability of the system.
Most of the current researches and patents only consider the influence of the temperature on the resistance of the rotor, and the resistance value of the rotor is considered to change slowly in the operation process of the motor. However, the rotor resistance is not only affected by temperature alone. Due to the skin effect, the rotor resistance is also affected by the rotor current frequency; due to the proximity effect, the rotor resistance is even further influenced by magnetic saturation of the rotor yoke and the rotor teeth. The approach effect is rapidly variable because it is influenced by magnetic saturation, which is influenced by magnetomotive force, which is determined by the stator and rotor currents. Therefore, the rotor resistance also changes rapidly in actual motor operation. If simply considering that the rotor resistance varies only with temperature, the accuracy of observation of the rotor flux linkage will be reduced.
More importantly, essentially all current research and patents are based on flux linkage observations made from linear models of induction motors, rather than saturation models of induction motors. The linear model of the induction motor completely ignores the saturation characteristic of the motor, resulting in the model not being consistent with the actual controlled object, which will further affect the observation accuracy of the rotor flux linkage.
Disclosure of Invention
The invention provides a method for high-precision online observation of rotor resistance and flux linkage of an induction motor, which is used for improving the observation precision of the rotor resistance and flux linkage of the induction motor and further improving the control performance and robustness of a system.
In order to solve the technical problem, the invention provides a method for high-precision online observation of the resistance and flux linkage of an induction motor rotor, which comprises the following steps:
1) Measuring necessary induction motor parameters;
off-line measurement of stator resistance R of induction motor s To fixLeakage inductance L sl Rotor leakage inductance L rl And the magnetization curve of the motor.
2) Considering a state equation of the induction motor with magnetic saturation under a column writing dq coordinate system;
3) Regarding a state equation of the induction motor as a column vector formed by functions, and performing Taylor expansion on the column vector;
the rotor resistance is considered as an independent variable, but not as a state variable of the system.
4) Building a PI controller for observing the resistance value of the rotor;
since the d-axis in the dq coordinate system is oriented to the rotor flux linkage, the q-axis component of the rotor flux linkage should be 0 if the coordinate system is oriented correctly. The design of the PI controller is carried out according to the principle.
As shown in fig. 2, the input of the PI controller is a comparison of the estimated q-axis of the rotor flux linkage with 0, and the output is an estimated value of the rotor resistance.
5) Building a Luenberger observer;
6) Calculating specific parameters of a matrix in the Roberter observer;
7) Calculating an observed value of the rotor flux linkage;
8) And calculating the slip electrical angular velocity and updating a matrix in the Luenberger observer.
An estimated value of the rotor flux linkage is obtained through step 7. Using this estimate, the collected stator current values i are combined sd The inductance of the induction motor can be calculated in real time.
Thus, all variables in the current calculation cycle have been updated. And repeating the calculation from the step 6 to the step 8. The flow is shown in FIG. 1.
The invention has the following beneficial effects: compared with the prior art, the method can complete high-precision online estimation of the rotor resistance and the rotor flux linkage of the induction motor through the steps, and can ensure that the dq coordinate system can be reliably oriented to the rotor flux linkage by utilizing the obtained high-precision rotor flux linkage observation value, so that the precision and the performance of vector control are improved.
Drawings
Fig. 1 is a system flow chart of a method for high-precision online observation of rotor resistance and flux linkage of an induction motor according to an embodiment of the invention.
Fig. 2 is a PI controller built to observe the rotor resistance value.
Fig. 3 is a first induction machine magnetization curve form.
Fig. 4 shows a magnetization curve pattern ii of the induction motor.
Fig. 5 is a view showing the observation result of the d-axis component of the rotor flux linkage.
Fig. 6 is a graph showing the observation result of the q-axis component of the rotor flux linkage.
Fig. 7 is a graph showing the observation result of the rotor resistance.
Fig. 8 is a dynamic graph of motor torque.
Fig. 9 is a dynamic graph of the rotational speed of the motor rotor.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1 to 8, the method for high-precision online observation of the resistance and flux linkage of the rotor of the induction motor provided by the invention comprises the following specific steps:
1) Measuring necessary induction motor parameters:
off-line measurement of stator resistance R of induction motor s Stator leakage inductance L sl And rotor leakage inductance L rl 。
And, the magnetization curve of the induction motor is measured off-line. The resulting magnetization curve is measured as in fig. 3, and then converted into the form shown in fig. 4.
In FIGS. 3 and 4, i m Is a magnetizing current; l is a radical of an alcohol m The mutual inductance between the stator and the rotor after dq transformation; psi is the flux linkage, i.e. Psi, psi = (L) in FIG. 4 m +L rl )×i m 。
And the rotating speed sensor is arranged on the rotor and is used for measuring the rotating speed of the rotor on line when the motor runs. If the induction motor is controlled by a control method without a rotating speed sensor, the estimated rotating speed signal of the rotor is used.
2) The equation of state of the induction machine considering magnetic saturation in the case of the column written dq coordinate system:
in this case, the stator current i is used s Magnetic linkage psi with rotor r The combination of (2) is described as an example of a state variable, and the state equation is shown in formula (1).
In the formula (1), u sd 、u sq D and q axis components of the stator voltage, respectively; i all right angle sd 、i sq D and q axis components of the stator current, respectively; psi rd 、ψ rq The d-axis component and the q-axis component of the rotor flux linkage are respectively; r s Is a stator resistor; r is r Is the rotor resistance; l is a radical of an alcohol sl Is the stator leakage inductance; l is a radical of an alcohol rl Is the rotor leakage inductance; l is a radical of an alcohol m The stator and the rotor are mutually inducted; omega 1 Synchronizing electrical angular velocity for the induction motor; omega s Is the slip electrical angular velocity. p is a differential operator.
And, in the formula (1),
and in the formula (1 a),
ψ＝L r i m ＝L r (i s +i r )＝ψ r +L rl i s (1d)
3) And regarding the state equation as a column vector consisting of functions, and performing Taylor expansion on the column vector:
writing the column of the formula (1) into a matrix form to obtain a formula (2)
Wherein x (t) = [ i ] sd i sq ψ rd ψ rq ] T ；u sr (t)＝[u sd u sq 0 0] T ；
Equation (2) is not in the form of a conventional equation of state, which is further organized into a conventional form.
At the same time, the rotor resistance R is adjusted r Stator-rotor mutual inductance L as a free variable m Viewed as a function determined by the state variable x, equation (3) may be further written as equation (4),
in the formula, f (x, R) r ,L m (x))＝-M -1 Nx；m(x,R r ,L m (x))＝M -1 u sr 。
The functional form of the equation of state is already obtained so that it can be subjected to taylor expansion. Here, the first element in the column vector of the state equation is taken as an example for explanation, and is listed in formula (5).
In the formula, xi represents a Taylor expansion point;
after taylor expansion of all elements of the state equation, the expanded formula column can be written in matrix form, see formula (6).
In the formula (I), the compound is shown in the specification,
and (5) further calculating the formula (6) to finally obtain a formula (7).
In the formula (I), the compound is shown in the specification,
4) Building a Longberger observer:
after a final matrix form of the system state equation after Taylor expansion is obtained, a Luenberger state detector is built according to a formula (7), namely a formula (8).
Wherein z is a 2 x 1 column vector; the matrix F is defined by the designer himself, here taking a diagonal matrix as an example,
definition of
Wherein λ is 1 And λ 2 Is the eigenvector of the matrix F;
5) Calculating specific parameters of a matrix in the Romberg observer:
equation (9) is used to compute the matrices T and K in the lunberg observer.
Columns are written in a specific element form, and for convenience of representation, the elements in the matrix A are denoted as a ij 。
The matrix T can be obtained by solving the following simple system of linear equations in two. Since the matrix F is self-defined by the designer, λ 1 And λ 2 In known amounts.
After obtaining the matrix T, the matrix K can be further obtained from equation (12).
After calculating to obtain the specific parameters of the matrix T and K, and
the calculation result obtained in the previous calculation cycle is updated, so that all elements in the formula (8) are known, and the value of the column vector z in the calculation cycle can be obtained through calculation.
6) Calculating an observed value of the rotor flux linkage:
after specific values of the column vector z are obtained through calculation, the matrix T obtained through calculation is combined with the stator current i collected through the current sensor sd The estimated value of the rotor flux linkage can be calculated by equation (13).
7) And constructing a PI controller for observing the resistance value of the rotor:
since the d-axis in the dq coordinate system is oriented to the rotor flux, the q-axis component of the rotor flux should be 0 if the coordinate system is oriented correctly. The design of the PI controller is carried out according to the principle.
As shown in fig. 2, the input of the PI controller is a comparison of the estimated q-axis of the rotor flux linkage with 0, and the output is an estimated value of the rotor resistance.
8) Calculating the slip electrical angular velocity, and updating the matrix M and N:
through step 6, an estimated value of the rotor flux linkage is obtained. Using this estimate, the collected stator current values i are combined sd The inductance of the induction motor can be calculated in real time.
First, the amplitude of the flux linkage ψ is calculated, which can be calculated by the following equation.
According to the obtained | ψ | and in combination with fig. 4, an | i | can be obtained by looking up a table on line m And obtaining Lambda and Lambda' through formulas (1 b) and (1 c), and obtaining stator-rotor mutual inductance L through calculation m . Wherein L is m The calculation is as follows.
Obtaining the estimated value of the rotor resistance and the stator-rotor mutual inductance L m Then, the real-time slip electrical angular velocity omega of the system can be calculated s And calculating as in formula (16).
After the real-time slip electrical angular velocity of the system is obtained, the synchronous electrical angular velocity of the system can be obtained by combining the rotor angular velocity value, the calculation is shown as a formula (17),
ω 1 ＝ω r +ω s (17)
wherein, ω is r Is the rotor electrical angular velocity.
Thus, all variables in the current calculation cycle have been updated, so that the updating of the matrices M, N can be performed according to equation (2) in preparation for the next calculation cycle. And repeating the calculation from the step 5 to the step 8. The flow chart can be seen in fig. 1.
Through the steps, the high-precision online estimation of the rotor resistance and the rotor flux linkage of the induction motor can be completed.
The specific parameters of the motor in this embodiment are as follows, i.e., leakage inductance L of the stator and the rotor sl ＝L rl =0.1mH; stator resistor R s =11m Ω; rotor resistance R r =2.5m Ω; the magnetization curves are shown in fig. 3 and 4. The matrix F in the Luenberger observer is set to
The proportional coefficient P in the PI controller is set to 0.2 and the integral coefficient I is set to 0.1. Stator current command is set as
So that the motor generates 40Nm of torque; the rotor is driven by a dc motor having a rotation speed control mode, the rotation speed of which is set to 500rpm.
During operation of the electric machine, the rotor resistance suddenly jumps from the nominal value to a nominal value of 2 times.
The observation results of the rotor flux linkage and the rotor resistance of the induction motor are shown in fig. 5-7, and it can be seen from the figures that the observation results have high consistency with the actual values, and the observation error of the rotor resistance is less than 2%.
As shown in fig. 8, when the rotor resistance fluctuates sharply, the dq coordinate system can be oriented to the rotor flux linkage quickly and reliably by the method of the present invention, and the torque fluctuation can be suppressed well.
As shown in fig. 9, since the torque fluctuation is well suppressed, the rotor rotation speed does not fluctuate significantly, thereby reducing the risk of mechanical failure of the system.
In conclusion, the method can complete high-precision online estimation of the rotor resistance and the rotor flux linkage of the induction motor, and ensure that the dq coordinate system can be reliably oriented to the rotor flux linkage by using the obtained high-precision rotor flux linkage observation value, thereby improving the precision and the performance of vector control.
The above description is only an example of the present invention, and is not intended to limit the present invention, and various modifications and changes may be made to the present invention by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.
Claims (1)
1. A method for high-precision online observation of the resistance and flux linkage of an induction motor rotor is characterized by comprising the following steps: the method comprises the following steps:
(1) Measuring necessary induction machine parameters: off-line measurement of stator resistance R of induction motor s Stator leakage inductance L sl Leakage inductance L with rotor rl Measuring the magnetization curve of the induction motor off line;
(2) Considering a state equation of the magnetically saturated induction motor under a column writing dq coordinate system;
(3) Considering the state equation as a column vector consisting of functions, equation (2) in matrix form is obtained:
wherein x (t) = [ i ] sd i sq ψ rd ψ rq ] T ；u sr (t)＝[u sd u sq 00] T ；
In the formula u sd 、u sq D and q axis components of the stator voltage, respectively; i all right angle sd 、i sq D-axis and q-axis components of the stator current, respectively; psi rd 、ψ rq Respectively the d and q axis components of the rotor flux linkage; r s Is a stator resistor; r r Is a rotor resistance; l is sl Is the stator leakage inductance; l is a radical of an alcohol rl Is the rotor leakage inductance; l is m The stator and the rotor are mutually inducted; omega 1 Synchronizing electrical angular velocity for the induction motor; omega s Is the slip electrical angular velocity; p is a differential operator;
the state equation is obtained after the state equation is arranged, the state equation of the induction motor saturation model is expanded by using a Taylor formula, and the rotor resistance is taken as an independent variable to finally obtain a formula (7);
in the formula (I), the compound is shown in the specification,
(4) Constructing a Luenberger observer, see formula (8);
wherein z is a 2 x 1 column vector; the matrix F is defined by the designer;
y is the output of the system, and the matrix T is defined by the designer; matrix of
(5) Calculating specific parameters of a matrix in the Luenberger observer: equation (9) is used to compute the matrices T and K in the Romberg observer;
(6) Calculating an observed value of the rotor flux linkage;
(7) Building a PI controller for observing the resistance value of the rotor;
(8) And calculating the slip electrical angular velocity and updating the matrixes M and N.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102208894A (en) * | 2011-03-16 | 2011-10-05 | 浙江理工大学 | Rotating speed evaluation method used for speed-sensorless induction motor vector controlling |
| CN108631677A (en) * | 2018-05-14 | 2018-10-09 | 山东理工大学 | A kind of automobile-used induction electromotor rotor resistance of low-speed electronic and stator resistance on-line identification method |
| CN110112969A (en) * | 2019-03-04 | 2019-08-09 | 吉林大学 | A kind of method of induction motor parameter on-line identification and compensation |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102208894A (en) * | 2011-03-16 | 2011-10-05 | 浙江理工大学 | Rotating speed evaluation method used for speed-sensorless induction motor vector controlling |
| CN108631677A (en) * | 2018-05-14 | 2018-10-09 | 山东理工大学 | A kind of automobile-used induction electromotor rotor resistance of low-speed electronic and stator resistance on-line identification method |
| CN110112969A (en) * | 2019-03-04 | 2019-08-09 | 吉林大学 | A kind of method of induction motor parameter on-line identification and compensation |
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